Average age of x and y is 20 years. If z were to replace x, average would be 19 and if z were to rep

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The average age of $x$ and $y$ is $20$ $years.$ If $z$ were to replace $x,$ the average would be $19$ and if $z$ were to replace $y$, the average would be $21.$ Find the ages of $x, y$ and $z$.

A

$22,18,20$

B

$18,22,20$

C

$22,18,20$

D

$18,20,22$

Solution

Sum of Age of $x$ and $y=40$ $years$

$y$ and $z=38$ $years,$ $Z$ and $X=42$ $years$

$x+y+z=\frac{40+38+42}{2}=\frac{120}{2}=60$

$x=60-38=22$ $years,$ $y=60-42=18$ $years$

$z=60-40=20$ $years$

Standard 13

Quantitative Aptitude

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